Question

The planes x + 2y + z = −4 and 3x + 3y − z = 3 meet in a line. how do i find a vector equation for that line?

Answer 1

solve for any 2 of the variables by eliminating the 3rd. The simplest of the possible answers can be solved by just adding the 2 equations resulting to: 4x + 5y = -1

Answer 2

find the normal vectors for the two planes...then compute the cross product for these two vectors. There resulting vector will be parallel to the equation of the line you want.